The previous chapter detailed the ED of of quantum scalar fields on a fixed curved background based in part on the efforts of Ipek, Abedi, and Caticha (IAC) in [1]}[2]}, which was itself inspired by the seminal works of Dirac [3]}[4]} as well as Hojman et al. [5]}, Kuchař [6]}, and Teitelboim [7]} [8]}(DHKT) in their development of covariant canonical methods in classical field theory. To recap, the key insight of DHKT was that a dynamics that unfolds in space-time must mirror a certain pattern, and that this pattern is itself reflective of the structure of surface deformations. As stressed by DHKT, the geometrical character of these conditions implies that they are of a rather universal nature and apply to any such dynamics. Thus, as shown earlier, ED can be made manifestly covariant by imposing just such a structure on the generators of ED. From this perspective, the covariant ED developed by IAC generalizes to the quantum domain the results of DHKT for classical fields evolving on a fixed background.
